The present invention relates to a simulator or a CAD (Computer Aided Design) system used widely for analysis and designing in all fields of advanced science and technologies including the nanometeric devices, the extremely high-speed fluid dynamics, the milliwave monolithic integrated circuits and the magnetic memory units, or more in particular to a method and a system for concurrent computing between heterogenous simulators in which heterogeneous simulators are efficiently coupled and a globally consistent solution is determined in order to analyze complicated physical phenomena, and which is capable of concurrent computing with an extremely high speed, a very high stability and a scalability. More specifically, the invention relates to an algorithm for the concurrent computing.
In the case where a simulator is used, the operator generally sets a parameter p for the material or structural modelling, the physical modelling or the numerical experimental modelling of the numerical calculation technique through an input display unit 1 including a mouse, a keyboard and a display, as shown in FIG. 6. According to this parameter p, a numerical calculation unit 3 including a CPU (Central Processing Unit), a memory and a network performs computations on a simulation program and determines a self-consistent solution of variables x, y of nonlinear simultaneous equations formed of the parameter p. The results of the variables x, y are displayed in the form of data or graphics on an output display unit 2 including a display unit and support the analysis and designing work by the operator.
In recent years, however, the science and technologies have made such a progress that the trend is toward more and more material and structural ramifications of systems to be analyzed and designed. At the same time, the physical mechanisms have been complicated to such an extent that the physical modelling and the numerical computation techniques are ever on the way of complication. For this reason, the critical problem faced by the engineers engaged in the development of simulators is that a program development schedule is delayed more and an enormous amount of time is required for numerical computations with the progress of complication of the physical model.
As shown in FIG. 6, assume that a simulator A has a parameter p and a variable x, and a simulator B has a parameter p and a variable y. Also, assume that the complication of the physical phenomena has formed a heterogeneous coupled equation 6 correlating the parameter p and the variables x, y. As a specific example, the general traditional fluid simulators are still applicable to substantially all the domains including the electrodes of the nanometeric devices. The very infinitesimal domains of the nanometeric structure, on the other hand, requires application of a quantum transportation simulator such as the tunnel effect. If means for using each simulator in the right way for the right applications is selected instead of restructuring an integral simulator applicable to the whole system, a coupled equation is formed which guarantees the current continuity in the boundary domain between the classic theory and the quantum theory. In "Contemporary Mathematics Vol. 157, pp. 377-398, 1994, J. F. Bourgat, et al., describe a coupled equation as a boundary condition and a problem of combination of Boltzmann equation and Euler equation or Navier Stokes equation to be applied to the extremely high-speed aerodynamics. The milliwave monolithic integrated circuits, for example, involves a general fluid simulator applicable to the electronic devices, a simulator based on the Maxwell equation applicable to the milliwave propagating in space and the coupled equation in the boundary domain. Further, a register simulator, a reproduce simulator and the coupled equation are formed for the register and reproduce simulation of magnetic memory. All of theme are the problems encountered in all the fields of advanced science and technologies with the progress of complication of the physical phenomena.
Normally, simulation engineers take the approach of structuring a program for a heterogeneous coupled equation 6 and combining a simulator A with a the simulator B. First, a parameter p is set in a numerical calculation unit 3 through an input display unit 1. A locally consistent solution x obtained from the simulator A and a locally consistent solution y obtained from the simulator B for the parameter p are sent to the heterogeneos coupled equation 6, which is solved to determine an increment .DELTA.p of the parameter p. A convergence decision unit 9 decides on the convergence of .DELTA.p. In the absence of convergence, a search vector setting unit 10 sets a new parameter p by increasing the parameter p by .DELTA.p. This process is repeated, and if a convergence is obtained, a value p, x, y of a globally consistent solution is displayed on an output display unit 2.
The method shown in FIG. 6 is called the uncoupled method. Since the heterogeneous coupled equation 6 can be developed individually, the program development involved is not so extensive, and each iteration requires only a small length of time. In view of the fact that the increment of the parameter p and the variables x, y are independently determined, however, the number of iterations increases, resulting in a very low convergence and a high risk of divergence.
On the other hand, the method shown in FIG. 7 is called the coupled method. In spite of a stable convergence obtained due to the dependent determination of the increment of the parameter p and the variables x, y, this method has the disadvantage that the restructuring of the heterogeneous coupled equation 6 including the simulator A and the simulator B greatly increases the scale of program development while at the same time considerably increasing the time required for each iteration.
In short, the above-mentioned decoupled method and the coupled method have the advantages and disadvantages in respect of stability and speed.